Spectropolarimetric signatures of Earth-like extrasolar planets

We present results of numerical simulations of the flux (irradiance), F, and the degree of polarization (i.e. the ratio of polarized to total flux), P, of light that is reflected by Earth-like extrasolar planets orbiting solar-type stars, as functions of the wavelength (from 0.3 to 1.0 micron, with 0.001 micron spectral resolution) and as functions of the planetary phase angle. We use different surface coverages for our model planets, including vegetation and a Fresnel reflecting ocean, and clear and cloudy atmospheres. Our adding-doubling radiative transfer algorithm, which fully includes multiple scattering and polarization, handles horizontally homogeneous planets only; we simulate fluxes and polarization of horizontally inhomogeneous planets by weighting results for homogeneous planets. Like the flux, F, the degree of polarization, P, of the reflected starlight is shown to depend strongly on the phase angle, on the composition and structure of the planetary atmosphere, on the reflective properties of the underlying surface, and on the wavelength, in particular in wavelength regions with gaseous absorption bands. The sensitivity of P to a planet's physical properties appears to be different than that of F. Combining flux with polarization observations thus makes for a strong tool for characterizing extrasolar planets. The calculated total and polarized fluxes will be made available through the CDS.Comment: 31 pages text, 17 figures, 1 table Submitted to A&

AGRICULTURE IN NORTHWEST MINNESOTA: ITS ROLE IN THE FUTURE OF THE REGION

Community/Rural/Urban Development,

NEW COMMUNITY WATER AND SEWER SYSTEMS AND THE POPULATION OF SMALL TOWNS

Public Economics,

Modeled flux and polarisation signals of horizontally inhomogeneous exoplanets, applied to Earth--like planets

We present modeled flux and linear polarisation signals of starlight that is reflected by spatially unresolved, horizontally inhomogeneous planets and discuss the effects of including horizontal inhomogeneities on the flux and polarisation signals of Earth-like exoplanets. Our code is based on an efficient adding--doubling algorithm, which fully includes multiple scattering by gases and aerosol/cloud particles. We divide a model planet into pixels that are small enough for the local properties of the atmosphere and surface (if present) to be horizontally homogeneous. Given a planetary phase angle, we sum up the reflected total and linearly polarised fluxes across the illuminated and visible part of the planetary disk, taking care to properly rotate the polarized flux vectors towards the same reference plane. We compared flux and polarisation signals of simple horizontally inhomogeneous model planets against results of the weighted sum approximation, in which signals of horizontally homogeneous planets are combined. Apart from cases in which the planet has only a minor inhomogeneity, the signals differ significantly. In particular, the shape of the polarisation phase function appears to be sensitive to the horizontal inhomogeneities. The same holds true for Earth-like model planets with patchy clouds above an ocean and a sandy continent. Our simulations clearly show that horizontal inhomogeneities leave different traces in flux and polarisation signals. Combining flux with polarisation measurements would help retrieving the atmospheric and surface patterns on a planet

Circular polarization signals of cloudy (exo)planets

The circular polarization of light that planets reflect is often neglected because it is very small compared to the linear polarization. It could, however, provide information on a planet's atmosphere and surface, and on the presence of life, because homochiral molecules that are the building blocks of life on Earth are known to reflect circularly polarized light. We compute $P_c$, the degree of circular polarization, for light that is reflected by rocky (exo)planets with liquid water or sulfuric acid solution clouds, both spatially resolved across the planetary disk and, for planets with patchy clouds, integrated across the planetary disk, for various planetary phase angles $\alpha$. The optical thickness and vertical distribution of the atmospheric gas and clouds, the size parameter and refractive index of the cloud particles, and $\alpha$ all influence $P_c$. Spatially resolved, $P_c$ varies between $\pm 0.20\%$ (the sign indicates the polarization direction). Only for small gas optical thicknesses above the clouds do significant sign changes (related to cloud particle properties) across the planets' hemispheres occur. For patchy clouds, the disk--integrated $P_c$ is typically smaller than $\pm 0.025\%$, with maximums for $\alpha$ between $40^\circ$ and $70^\circ$, and $120^\circ$ to $140^\circ$. As expected, the disk--integrated $P_c$ is virtually zero at $\alpha=0^\circ$ and 180$^\circ$. The disk--integrated $P_c$ is also very small at $\alpha \approx 100^\circ$. Measuring circular polarization signals appears to be challenging with current technology. The small atmospheric circular polarization signal could, however, allow the detection of circular polarization due to homochiral molecules. Confirmation of the detectability of such signals requires better knowledge of the strength of circular polarization signals of biological sources.Comment: 15 pages, 11 figures, Accepted for publication in Astronomy and Astrophysic

The O2 A-band in fluxes and polarization of starlight reflected by Earth-like exoplanets

Earth-like, potentially habitable exoplanets are prime targets in the search for extraterrestrial life. Information about their atmosphere and surface can be derived by analyzing light of the parent star reflected by the planet. We investigate the influence of the surface albedo $A_{\rm s}$, the optical thickness $b_{\rm cloud}$ and altitude of water clouds, and the mixing ratio $\eta$ of biosignature O$_2$ on the strength of the O$_2$ A-band (around 760 nm) in flux and polarization spectra of starlight reflected by Earth-like exoplanets. Our computations for horizontally homogeneous planets show that small mixing ratios ($\eta$ < 0.4) will yield moderately deep bands in flux and moderate to small band strengths in polarization, and that clouds will usually decrease the band depth in flux and the band strength in polarization. However, cloud influence will be strongly dependent on their properties such as optical thickness, top altitude, particle phase, coverage fraction, horizontal distribution. Depending on the surface albedo, and cloud properties, different O$_2$ mixing ratios $\eta$ can give similar absorption band depths in flux and band strengths in polarization, in particular if the clouds have moderate to high optical thicknesses. Measuring both the flux and the polarization is essential to reduce the degeneracies, although it will not solve them, in particular not for horizontally inhomogeneous planets. Observations at a wide range of phase angles and with a high temporal resolution could help to derive cloud properties and, once those are known, the mixing ratio of O$_2$ or any other absorbing gas.Comment: 21 pages, 20 figures, accepted for publication in Ap

Blue, white, and red ocean planets - Simulations of orbital variations in flux and polarization colors

An exoplanet's habitability will depend strongly on the presence of liquid water. Flux and/or polarization measurements of starlight that is reflected by exoplanets could help to identify exo-oceans. We investigate which broadband spectral features in flux and polarization phase functions of reflected starlight uniquely identify exo-oceans. We compute total fluxes F and polarized fluxes Q of starlight reflected by cloud-free and (partly) cloudy exoplanets, for wavelengths from 350 to 865 nm. The ocean surface has waves composed of Fresnel reflecting wave facets and whitecaps, and scattering within the water body is included. Total flux F, polarized flux Q, and degree of polarization P of ocean planets change color from blue, through white, to red at phase angles alpha ranging from 134-108 deg for F, and from 123-157 deg for Q, with cloud coverage fraction fc increasing from 0.0 to 1.0 for F, and to 0.98 for Q. The color change in P only occurs for fc ranging from 0.03-0.98, with the color crossing angle alpha ranging from 88-161 deg. The total flux F of a cloudy, zero surface albedo planet can also change color, and for fc=0.0, an ocean planet's F will not change color for surface pressures ps > 8 bars. Polarized flux Q of a zero surface albedo planet does not change color for any fc. The color change of P of starlight reflected by an exoplanet, from blue, through white, to red with increasing alpha above 88 deg, appears to identify a (partly) cloudy exo-ocean. The color change of polarized flux Q with increasing alpha above 123 deg appears to uniquely identify an exo-ocean, independent of surface pressure or cloud fraction. At the color changing phase angle, the angular distance between a star and its planet is much larger than at the phase angle where the glint appears in reflected light. The color change in polarization thus offers better prospects for detecting exo-oceans.Comment: Accepted for publication in Astron. Astrophys; multicolumn versio

The influence of forward-scattered light in transmission measurements of (exo)planetary atmospheres

[Abridged] The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scattering particles. Here, we present results of calculations with a three-dimensional Monte Carlo code that simulates the transmitted flux during occultations or transits. For isotropically scattering particles, like gas molecules, the transmitted flux appears to be well-described by the total atmospheric optical thickness. Strongly forward-scattering particles, however, such as commonly found in atmospheres of Solar System planets, can increase the transmitted flux significantly. For exoplanets, such added flux can decrease the apparent radius of the planet by several scale heights, which is comparable to predicted and measured features in exoplanet transit spectra. We performed detailed calculations for Titan's atmosphere between 2.0 and 2.8 micron and show that haze and gas abundances will be underestimated by about 8% if forward-scattering is ignored in the retrievals. At shorter wavelengths, errors in the gas and haze abundances and in the spectral slope of the haze particles can be several tens of percent, also for other Solar System planetary atmospheres. We also find that the contribution of forward-scattering can be fairly well described by modelling the atmosphere as a plane-parallel slab.Comment: Icarus, accepted for publicatio

PyMieDAP: a Python--Fortran tool to compute fluxes and polarization signals of (exo)planets

PyMieDAP (the Python Mie Doubling-Adding Programme) is a Python--based tool for computing the total, linearly, and circularly polarized fluxes of incident unpolarized sun- or starlight that is reflected by, respectively, Solar System planets or moons, or exoplanets at a range of wavelengths. The radiative transfer computations are based on an adding--doubling Fortran algorithm and fully include polarization for all orders of scattering. The model (exo)planets are described by a model atmosphere composed of a stack of homogeneous layers containing gas and/or aerosol and/or cloud particles bounded below by an isotropically, depolarizing surface (that is optionally black). The reflected light can be computed spatially--resolved and/or disk--integrated. Spatially--resolved signals are mostly representative for observations of Solar System planets (or moons), while disk--integrated signals are mostly representative for exoplanet observations. PyMieDAP is modular and flexible, and allows users to adapt and optimize the code according to their needs. PyMieDAP keeps options open for connections with external programs and for future additions and extensions. In this paper, we describe the radiative transfer algorithm that PyMieDAP is based on and the code's principal functionalities. And we provide benchmark results of PyMieDAP that can be used for testing its installation and for comparison with other codes. PyMieDAP is available online under the GNU GPL license at http://gitlab.com/loic.cg.rossi/pymiedapComment: 15 pages, 7 figures, 4 tables. Accepted for publication in Astronomy and Astrophysic